Abstract: A digital synthesizer for producing a digital frequency signal includes a phase accumulator for repeatedly accumulating a phase value to generate samples of a digital sawtooth signal and a look-up table of digital samples for converting the digital sawtooth signal to a digital waveshape signal. In order to reduce the effect of the quantization of the digital samples, the synthesizer also includes a randomizer for applying a randomizing factor to output digital samples for forming the digital frequency signal. The randomizer includes a randomizing factor generator connected to receive P bits of each digital sample for generating at least one randomizing bit and an summer for summing the remaining N bits of the digital sample and the at least one randomizing bit to generate a digital waveshape sample of the digital frequency signal.